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Discrete Reasoning Puzzles

These puzzles require sharp, logical thinking. Can you solve them?


An Arab sheikh is old and must will his fortune to one of his two sons. He makes a proposition. His two sons will ride their camels in a race, and whichever camel crosses the finish line last will win the fortune for its owner. During the race, the two brothers wander aimlessly for days, neither willing to cross the finish line. In desperation, they ask a wise man for advice. He tells them something; then the brothers leap onto the camels and charge toward the finish line. What did the wise man say?



You have a jug that holds five gallons, and a jug that holds three gallons. You have no other containers, and there are no markings on the jugs. You need to obtain exactly seven gallons of water from a faucet. How can you do it?

Second Problem: You need exactly four gallons. How do you do it?



You are on a game show. You are shown three closed doors. A prize is hidden behind one, and the game show host knows where it is. You are asked to select a door. You do. Before you open it, the host opens one of the other doors, showing that it is empty, then asks you if you'd like to change your guess. Should you, should you not, or doesn't it matter?



A farmer is taking a fox, a chicken, and a bag of grain home. To get there, he must cross a river, but he's only allowed to take one item across the bridge with them at a time. If the fox is left alone with the chicken, the fox will eat the chicken. If the chicken is left alone with the grain, the chicken will eat the grain. How can the farmer cross the river without any of his possessions being eaten?



Travelling to a city, an old man lost his way. He came to a fork in the road and did not know which road to take. Standing at the fork were two men. Next to the men was a sign, which you may assume is correct, which stated that one of the two men always told the truth and one of the men always told lies (but it was not known which was which). The sign went on to say that travellers could only ask one of the men one question.

What question could the old man pose that would give him the information he needs to choose the correct route?



You are given eight jelly doughnuts. The doughnuts all weigh the same amount except for one which is heavier. You have a balancing scale at your disposal. What's the minimum number of weighings required for you to pick out the heavy doughnut every time?



Three men stay at a hotel for the night. The innkeeper charges thirty dollars per room per night. The men rent one room; each pays ten dollars. The bellhop leads the men to their room. Later, the innkeeper discovers he has overcharged the men and asks the bellhop to return five dollars to them. On the way upstairs, the bellhop realizes that five dollars can't be evenly split among three men, so he decides to keep two dollars for himself and return one dollar to each man.

At this point, the men have paid nine dollars each, totalling 27. The bellhop has two, which adds up to 29. Where did the thirtieth dollar go?



Three men, members of a safari, are captured by cannibals in the jungle. The men are given one chance to escape with their lives. The men are lined up and bound to stakes such that one man can see the backs of the other two, the middle man can see the back of the front man, and the front man can't see anybody. The men are shown five hats, three of which are black and two of which are white. Then the men are blindfolded, and one of the five hats is placed on each man's head. The remaining two hats are hidden away. The blindfolds are removed. The men are told that if just one of the men can guess what hat he's wearing, they may all go free. Time passes. Finally, the front man, who can't see anyone, correctly guesses the color of his hat. What color was it, and how did he guess correctly?



One day a girl celebrated her birthday. Two days later, her older twin brother celebrated his. How is this possible?



Tough one!

You and your spouse invite four other couples to a party. During the course of the conversation, it is discovered that, prior to the party, each person except you was acquainted with a different number of the people present. Assuming the acquaintance relationship is symmetric (i.e., if you are acquainted with someone, that person is also acquainted with you), then how many people did your spouse know prior to the party? How many people did you know?